Channel estimation for wireless systems with multiple transit antennas

ABSTRACT

In various embodiments, techniques are provided to determine channel characteristics of various communication systems such as OFDM systems or systems using a plurality of transmit antennas by using various sets of training symbols.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of copending U.S. patent applicationSer. No. 09/861,811 filed on May 21, 2001 entitled “CHANNEL ESTIMATIONFOR WIRELESS SYSTEMS WITH MULTIPLE TRANSIT ANTENNAS” the contents ofwhich are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of Invention

This invention relates to channel estimation in wireless systems.

2. Description of Related Art

As wireless communications systems are deployed around the world, theimportance of providing clear and cost-effective communication servicesincreases. Unfortunately, providing clear communications can requiremitigating various obstacles such as inter-symbol-interference (ISI). Toreduce ISI, a technique known as orthogonal frequency divisionmultiplexing (OFDM) can be used. Orthogonal frequency divisionmultiplexing is a communication paradigm where a single communicationchannel is divided into many narrow sub-bands, which then can betransmitted in parallel. By transmitting symbols in this fashion, theduration of each symbol can be dramatically increased, which can greatlyreduce or completely eliminate ISI problems.

Unfortunately, individual sub-bands within an OFDM transmission aresubject to Rayleigh fading, especially when used in mobile communicationsystems. While the effects of Rayleigh fading can be mitigated by usingmultiple transmitter and/or receiver antennas, estimating the channelcharacteristics for all transmitter-receiver antenna pairs can bedifficult and computationally intensive. Accordingly, there is a needfor apparatus and techniques that provide for better channel estimation.

SUMMARY OF THE INVENTION

In various embodiments, techniques are provided to determine channelcharacteristics of various communication systems such as OFDM systems orsystems using a plurality of transmit antennas.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is described in detail with regard to the followingfigures, wherein like numerals reference like elements, and wherein:

FIG. 1 is a block diagram of an exemplary communication system;

FIG. 2 depicts an OFDM signal having multiple sub-bands;

FIG. 3 depicts an exemplary communication signal of an OFDM sub-band;

FIG. 4 is a block diagram of an equalizer with an exemplary channelestimator;

FIG. 5 is a block diagram of the exemplary channel estimator of FIG. 4;and

FIG. 6 is a flowchart outlining an exemplary technique for estimatingcommunication channels.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

For wireless systems, channel estimation can be difficult andcomputationally intensive. For wireless communication systems such asorthogonal frequency division multiplexing (OFDM) systems that usemultiple sub-bands, computational costs can increase since each sub-bandmust be estimated. Furthermore, because practical OFDM systems canrequire multiple transmit and/or receive antennas, the computationalcosts can rise to enormous levels as each sub-band for eachtransmit/receive antenna pair must be estimated.

Regardless of such computational costs, the difficulty of channelestimation is further complicated in the context of mobile systemsbecause the characteristics of mobile channels can continually changeover time. Thus, even if every OFDM sub-band for every transmit/receiveantenna pair is accurately modeled at the start, middle or end of acommunication, such channel estimates can be totally inadequate forother portions of the communication.

Generally, a mobile channel can be estimated by embedding a set ofpredetermined symbols known as training symbols at a transmitter andprocessing the training symbols at a receiver to produce a set ofinitial channel estimates. For continually changing channels such asmobile channels, the initial channel estimates can then be iterativelyupdated, or adapted, over time by appropriately processing subsequentdata symbols. For example, a set of training symbols in a receivedsignal can be used to estimate a set of initial channel estimates {tildeover (H)}[n] that, in turn, can be used to equalize the received signal.The set of initial channel estimates {tilde over (H)}[n] can then beupdated using the equalized received signal to adapt the channelestimates to track the changing channel environment, i.e., {tilde over(H)}[n+1]=Φ[{tilde over (H)}[n]] where Φ is some predetermined functionand n+1 relates to a frame of data processed after frame n.

Unfortunately, determining the various sets of channel estimates forcommunication systems having multiple antennas can require the formationand use of a cross-correlation matrix Q that must be subsequentlyinverted. As the size of the cross-correlation matrix Q grows, thecomputational requirements to invert Q can grow geometrically. Whilejudiciously choosing training symbols can eliminate the need to invertthe cross-correlation matrix Q, data symbols, unlike training symbols,cannot be so chosen.

However, by making various assumptions about the data symbols, sets ofupdated channel estimates can be estimated without inverting thecross-correlation matrix Q, and computational costs can be vastlyreduced with only a minor degradation in the accuracy of the channelestimates.

FIG. 1 is a block diagram of an exemplary transmission system 100. Thetransmission system 100 includes an encoder 110 having a number ofassociated OFDM transmitters 120-1, 120-2, . . . 120-N and respectivetransmit antennas 130-1, 130-2, . . . 130-N, and an equalizer 160 havinga number of associated OFDM receivers 150-1, 150-2, . . . 150-M withrespective receive antennas 140-1, 140-2, . . . 140-M.

In operation, the encoder 110 can form blocks of symbols that can beprovided to the various OFDM transmitters 120-1, 120-2, . . . 120-N. Thevarious OFDM transmitters 120-1, 120-2, . . . 120-N, in turn, canmodulate the blocks of symbols into electromagnetic carriers such asradio-frequency waves that can then be transmitted using theirrespective transmitting antennas 130-1, 130-2, . . . 130-N. The variousradio-frequency signals 135 can then be received by the receive antennas140-1, 140-2, . . . 140-M and fed to their respective OFDM receivers150-1, 150-2, . . . 150-M. The OFDM receivers 150-1, 150-2, . . . 150-Mcan then transform the received radio-frequency signals 135 intobase-band signals, digitize the base-band signals and provide thedigitized base-band signals to the equalizer 160. The equalizer 160, inturn, can extract the symbols from the digitized base-band signals andperform various operations on the symbols.

As shown in FIG. 1, the radio-frequency signals 135 transmitted by eachtransmit antenna 130-1, 130-2, . . . 130-N can be subsequently receivedby each of the receiving antennas 140-1, 140-2, . . . 140-M. While FIG.1 depicts the various communication channels as single direct pathsbetween each transmit/receive antenna pair, it should be appreciatedthat each radio-frequency signal 135 can propagate from each transmitantenna 130-1, 130-2, . . . 130-N to each receive antenna 140-1, 140-2,. . . 140-M not only through a direct path, but can also propagate fromeach transmit antenna 130-1, 130-2, . . . 130-N to each receive antenna140-1, 140-2, . . . 140-M through a variety of indirect paths (notshown).

The various radio-frequency signal paths for a particulartransmit/receive antenna pair can produce a complex communicationchannel, which can be distinctly different from any other communicationchannel defined by another transmit/receive antenna pair. Generally, thechannel characteristics of an individual mobile wireless channel i.e.,the impulse response, can be described by Eq.(1): $\begin{matrix}{{{h\left( {t,\tau} \right)} = {\sum\limits_{k}{{\gamma_{k}(t)}{c\left( {\tau - \tau_{k}} \right)}}}},} & (1)\end{matrix}$where τ_(k) is the delay of the k-th path, γ_(k)(t) is the correspondingcomplex amplitude for the k-th path, and c(t) is the shaping pulse forthe k-th path whose frequency response is usually a square-root raisedcosine Nyquist filter. When a communication channel is a mobile wirelesschannel, the motion of a vehicle can affect the complex amplitudesγ_(k)(t)'s, making each complex amplitude γ_(k)(t) a wide-sensestationary (WSS), narrow-band complex Gaussian process, that can beindependent for different signal paths.

From Eq. (1), the frequency response H(t, f) of a communication channelat time t can be described by Eq. (2): $\begin{matrix}{{H\left( {t,f} \right)}\overset{\Delta}{=}{\int_{- \infty}^{+ \infty}{{h\left( {t,\tau} \right)}{\exp\left( {{- j}\quad 2\pi\quad f\quad\tau} \right)}{\mathbb{d}\tau}\quad{or}}}} & (2) \\{\quad{{\overset{\Delta}{=}{{C(f)}{\sum\limits_{k}{{\gamma_{k}(t)}{\exp\left( {{- j}\quad 2\pi\quad f\quad\tau_{k}} \right)}}}}}{where}}} & (3) \\{{C(f)}\overset{\Delta}{=}{\int_{- \infty}^{+ \infty}{{c(\tau)}{{\exp\left( {{- j}\quad 2\quad\pi\quad f\quad\tau_{k}} \right)}.}}}} & (4)\end{matrix}$

For OFDM systems with proper cyclic extension and timing, the channelfrequency response can be expressed by Eq.(5): $\begin{matrix}{{H\left\lbrack {n,k} \right\rbrack} = {{H\left( {{nT}_{f},{k\quad\Delta\quad f}} \right)} = {\sum\limits_{t = 0}^{K_{o} - 1}{{h\left\lbrack {n,l} \right\rbrack}W_{K}^{kl}}}}} & (5)\end{matrix}$where h[n, l]

h(nT_(f), kT_(f)/K), W_(K) ^(kl)=exp(−j2πkl/K), K is the number ofsub-bands (tones) in an OFDM block, k is an index designating aparticular sub-band, l is a time domain index, T_(f) is the block lengthand Δf is the sub-band (tone) spacing.

Following Eq. (5), the frequency response at the k-th tone of an n-thblock of OFDM symbols corresponding to an i-th transmit antenna can beexpressed by Eq.(6): $\begin{matrix}{{H_{i}\left\lbrack {n,k} \right\rbrack} = {\sum\limits_{l = 0}^{K_{o} - 1}{{h_{i}\left\lbrack {n,l} \right\rbrack}{W_{K}^{kl}.}}}} & (6)\end{matrix}$

Equation (6) demonstrates that H_(i)[n, k] can be obtained by estimatingor otherwise acquiring h_(i)[n, k]. Accordingly, the received signalr[n, k] at each receive antenna 140-1, 140-2, . . . 140-M can beexpressed by Eq. (7):r[n,k]=Σ ^(M) _(i−1) H _(i) [n,k]t _(i) [n,k]+w[n,k],  (7)where M is the number of transmit antennas, k denotes a particular OFDMsub-band and k=0, 1, . . . , K−1 for all n blocks. If the transmittedsignals t_(i)[n, k]'s from each transmit antenna contain known signalssuch as training symbols, the temporal estimation of the variouscommunication channels h_(i)[n, l]'s can be derived using Eq. (8):$\begin{matrix}{{{\begin{pmatrix}{Q_{11}\lbrack n\rbrack} & {Q_{12}\lbrack n\rbrack} & \cdots & {Q_{1P}\lbrack n\rbrack} \\{Q_{21}\lbrack n\rbrack} & {Q_{22}\lbrack n\rbrack} & \quad & \vdots \\\vdots & \quad & ⋰ & \quad \\{Q_{P1}\lbrack n\rbrack} & \cdots & \quad & {Q_{PP}\lbrack n\rbrack}\end{pmatrix}\begin{pmatrix}{{\overset{\sim}{h}}_{1}\lbrack n\rbrack} \\{{\overset{\sim}{h}}_{2}\lbrack n\rbrack} \\\vdots \\{{\overset{\sim}{h}}_{P}\lbrack n\rbrack}\end{pmatrix}} = \begin{pmatrix}{p_{1}\lbrack n\rbrack} \\{p_{2}\lbrack n\rbrack} \\\vdots \\{p_{P}\lbrack n\rbrack}\end{pmatrix}},{or}} & (8) \\{{\begin{pmatrix}{{\overset{\sim}{h}}_{1}\lbrack n\rbrack} \\{{\overset{\sim}{h}}_{2}\lbrack n\rbrack} \\\vdots \\{{\overset{\sim}{h}}_{P}\lbrack n\rbrack}\end{pmatrix} = {\begin{pmatrix}{Q_{11}\lbrack n\rbrack} & {Q_{12}\lbrack n\rbrack} & \cdots & {Q_{1P}\lbrack n\rbrack} \\{Q_{21}\lbrack n\rbrack} & {Q_{22}\lbrack n\rbrack} & \quad & \vdots \\\vdots & \quad & ⋰ & \quad \\{Q_{P1}\lbrack n\rbrack} & \cdots & \quad & {Q_{PP}\lbrack n\rbrack}\end{pmatrix}^{- 1}\begin{pmatrix}{p_{1}\lbrack n\rbrack} \\{p_{2}\lbrack n\rbrack} \\\vdots \\{p_{P}\lbrack n\rbrack}\end{pmatrix}}},} & (9)\end{matrix}$where{tilde over (h)} _(i) [n]( {tilde over (h)} _(i) [n,0]. . . , {tildeover (h)} _(i) [n,K _(o)−1])^(T),  (10)Q _(ij) [n]

(q _(ij) [n,i−j])_(i,j=1) ^(K) ^(o) , and  (11)p _(i) [n]

(p _(i) [n,0], . . . , p _(i) [n,K _(o) −1]) ^(T)  (12)where {tilde over (h)}_(i)[n] is the estimated channel impulse responsefor the channel between an i-th transmit antenna and a particularreceive antenna, Q_(ij)[n] is the correlated energy between the set oftraining symbols t_(i)[n, k] of an i-th transmit antenna and the set oftraining symbols t_(j)[n, k] of a j-th transmit antenna and p_(i)[n] isthe cross-correlation vector between the set of training symbolst_(i)[n, k] of an i-th transmit antenna and a received signal r[n, k] ata particular receive antenna, and where: $\begin{matrix}{{{q_{ij}\left\lbrack {n,l} \right\rbrack}\overset{\Delta}{=}{\sum\limits_{k = 0}^{K - 1}{{t_{i}\left\lbrack {n,k} \right\rbrack}{t_{j}^{*}\left\lbrack {n,k} \right\rbrack}W_{K}^{- {kl}}}}},\text{or~~alternatively,}} & (13) \\{{{q_{ij}\left\lbrack {n,l} \right\rbrack}\overset{\Delta}{=}{{IFFT}\left\{ {{t_{i}\left\lbrack {n,k} \right\rbrack}{t_{j}^{*}\left\lbrack {n,k} \right\rbrack}} \right\}}},{and}} & (14) \\{{{p_{i}\left\lbrack {n,l} \right\rbrack}\overset{\Delta}{=}{\sum\limits_{k = 0}^{K - 1}{{r\left\lbrack {n,k} \right\rbrack}{t_{j}^{*}\left\lbrack {n,k} \right\rbrack}W_{K}^{- {kl}}}}},\text{or~~alternatively,}} & (15) \\{{p_{i}\left\lbrack {n,l} \right\rbrack}\overset{\Delta}{=}{{IFFT}{\left\{ {{r\left\lbrack {n,k} \right\rbrack}{t_{i}^{*}\left\lbrack {n,k} \right\rbrack}} \right\}.}}} & (16)\end{matrix}$From Eqs. (8) and (9), one can see that a matrix inversion is requiredto get the temporal estimation of each channel impulse response h_(i)[n,k], i.e., {tilde over (H)}=Q⁻¹ P.

FIG. 2 depicts an exemplary OFDM signal 200 displayed along a time axis210 and against a frequency axis 220. As shown in FIG. 2, the OFDMsignal 200 contains a number of individual sub-bands (tones) 230-1,230-2, . . . 230-K with each respective sub-band centered on arespective one of closely spaced frequencies f₁, f₂, . . . f_(K). FIG. 3depicts an exemplary communication signal 300 capable of being embeddedin the various sub-bands of FIG. 2. As shown in FIG. 3, thecommunication signal 300 contains a number of sync symbols 310, a numberof training symbols 320, a number of data symbols 330 and a number ofguard symbols 340.

Data symbols, also known as payload symbols, can contain information tobe transmitted. Guard symbols are symbols that can pad either or both ofthe beginning and end of a burst transmission and can be used for avariety of purposes including providing buffering, timing andsynchronization. Sync symbols are predetermined symbols placed atvarious strategic positions within a block of data that can allow areceiver to synchronize or otherwise extract timing information from atransmitted signal.

Training symbols, like sync symbols, can be predetermined symbols placedat known positions. However, unlike sync symbols, training symbols areusually configured to enable an equalizer to estimate a givencommunication channel. It should be appreciated that, in variousexemplary embodiments, the training symbols 320 can be any set ofsymbols suitable for training an equalizer. For example, the exemplarytraining symbols 320 can be formed taking into account various factorssuch as their suitability for clock recovery, frequency-shiftestimation, their peak-to-average ratio of signal strength or any otherknown or later recognized factor useful for generating an advantageousor otherwise adequate training sequence.

As discussed above, training symbols can be selected such that invertingthe cross-correlation matrix Q in Eq. (8) can be simplified. Forexample, various sets of training symbols can be selected such that acorrelation between two different sets of training symbols is zero, thusreducing Eq. (9) above to the form of Eq. (17) below: $\begin{matrix}{\begin{pmatrix}{{\overset{\sim}{h}}_{1}\lbrack n\rbrack} \\{{\overset{\sim}{h}}_{2}\lbrack n\rbrack} \\\vdots \\{{\overset{\sim}{h}}_{i}\lbrack n\rbrack}\end{pmatrix} = {\begin{pmatrix}{Q_{11}\lbrack 0\rbrack} & 0 & \cdots & 0 \\0 & {Q_{22}\lbrack 1\rbrack} & \quad & 0 \\\vdots & \quad & ⋰ & \vdots \\0 & 0 & \cdots & {Q_{ij}\lbrack n\rbrack}\end{pmatrix}^{- 1}{\begin{pmatrix}{p_{1}\lbrack n\rbrack} \\{p_{2}\lbrack n\rbrack} \\\vdots \\{p_{i}\lbrack n\rbrack}\end{pmatrix}.}}} & (17)\end{matrix}$

Because all off-axis elements of the Q matrix are zero, determining theinverse matrix Q⁻¹ can be greatly simplified. Furthermore, when thevarious transmitted signals are transmitted using a constant-modulustechnique such as quadrature amplitude modulated (QAM), the absolutevalues of any transmitted symbols will be equal to one, i.e., (|t_(i)[n,k]=1), the cross-correlation matrix Q can be reduced to Q=K×I, for alli=1, 2, . . . N, and Eq. (17) can be further reduced to the form of Eq.(18): $\begin{matrix}{{\begin{pmatrix}{{\overset{\sim}{h}}_{1}\lbrack n\rbrack} \\{{\overset{\sim}{h}}_{2}\lbrack n\rbrack} \\\vdots \\{{\overset{\sim}{h}}_{i}\lbrack n\rbrack}\end{pmatrix} = {\begin{pmatrix}K & 0 & \cdots & 0 \\0 & K & \quad & \vdots \\\vdots & \quad & ⋰ & 0 \\0 & \cdots & 0 & K\end{pmatrix}^{- 1}\begin{pmatrix}{p_{1}\lbrack n\rbrack} \\{p_{2}\lbrack n\rbrack} \\\vdots \\{p_{i}\lbrack n\rbrack}\end{pmatrix}}},{or}} & (18) \\{\begin{pmatrix}{{\overset{\sim}{h}}_{1}\lbrack n\rbrack} \\{{\overset{\sim}{h}}_{2}\lbrack n\rbrack} \\\vdots \\{{\overset{\sim}{h}}_{i}\lbrack n\rbrack}\end{pmatrix} = {\begin{pmatrix}1 & 0 & \cdots & 0 \\0 & 1 & \quad & \vdots \\\vdots & \quad & ⋰ & 0 \\0 & \cdots & 0 & 1\end{pmatrix}^{- 1}\begin{pmatrix}{p_{1}\lbrack n\rbrack} \\{p_{2}\lbrack n\rbrack} \\\vdots \\{p_{i}\lbrack n\rbrack}\end{pmatrix}}} & (19)\end{matrix}$

Accordingly, the problem of determining channel characteristics can bereduced to solving Eq. (20): $\begin{matrix}{{{h_{i}\left\lbrack {n,l} \right\rbrack} = {\frac{1}{K}{p_{i}\left\lbrack {n.l} \right\rbrack}}},\text{or~~alternatively}} & (20) \\{{h_{i}\left\lbrack {n,l} \right\rbrack} = {\frac{1}{K}{p_{1}\left\lbrack {n,{l - {\left( {i - 1} \right){\overset{\_}{K}}_{o}}}} \right\rbrack}}} & (21)\end{matrix}$for l=0, . . . , {overscore (K)}₀−1, where {overscore (K)}₀ is a numberof samples and i=1, 2 . . . , N. Further details about the exemplarytraining symbols can be found in at least “Optimum training Sequencesfor Wireless Systems” by Ye LI (U.S. patent application Ser. No. ______,(Attorney Docket 1999-0759, 105493) concurrently filed and commonlyassigned) incorporated herein by reference in its entirety including allreferences cited therein.

Returning to FIG. 3, it should be appreciated that, while the exemplarycommunication signal 300 is a burst signal with a particular form, itshould be appreciated that the form of a burst signal can vary withoutdeparting from the spirit and scope of the present invention. Forexample, it should be appreciated that the training symbols 320 can bedispersed intermittently within the payload symbols 330. It shouldfurther be appreciated that while the exemplary communication signal 300is a burst signal, the communication signal 300 can take various otherforms such as a continuous signal in which various training symbols canbe periodically embedded.

FIG. 4 is a block diagram of the exemplary equalizer 160 of FIG. 1. Theexemplary equalizer 160 includes a diversity gain processor 610 and achannel estimator 620.

In operation, the diversity gain processor 610 and channel estimator 620can each receive various received signals r₁[n, k], r₂[n, k], . . .r_(M)[n, k] such as blocks of symbols from OFDM transmissions via links152-1, 152-2, . . . 152-M. The channel estimator 620 can then determinea set of initial channel estimates for each communication channelbetween a transmit/receive antenna pair.

As discussed above, each of the received signals r_(i)[n, k] can containmultiple transmit signals t_(i)[n, k]'s according to Eq. (7) abovetransmitted by a plurality of transmit antennas, with each transmitsignal t_(i)[n, k] having an assortment of sync symbols, trainingsymbols, data symbols and guard symbols, as well as any other symboltypes. Also as discussed above, the training symbols embedded in thecommunication signals for each of the transmit signals t_(i)[n, k] canbe known symbol patterns and formed such that there is essentially nocross-correlated energy between each set of training symbols, i.e.,q_(ij)[n, l]=0 for all i≠j such that a set of initial channel estimatescan be determined using Eq. (18) above. Furthermore, when a QAM or otherconstant-modulus approach is used, a set of initial channel estimatescan be determined using Eqs. (20) or (21) above. However, the particularform and respective computational efficiency of the training symbols canvary and can include any combination or sequence of symbols that can beused to determine the characteristic estimates of a communicationchannel without departing from the spirit and scope of the presentinvention.

While the exemplary estimator 620 can use a set of training symbols todetermine a set of initial channel estimates, it should be appreciatedthat the estimator 620 can alternatively use any other symbol type,including data symbols, to determine sets of initial channel estimates.Still further, it should be appreciated that the exemplary estimator 160can use any other known or later developed technique suitable to produceinitial channel estimates without departing from the spirit and scope ofthe present invention.

After the communication channels have been initially characterized, thechannel estimator 620 can export the sets of initial channel estimatesto the diversity gain processor 610, which can use the sets of channelestimates to provide spatial and temporal equalization on the receivedsignals and produce streams of symbol decisions t′_(i)[n, k] that can beexported to an external device (not shown) via link 162 and/or exportedto the channel estimator 620 via links 612-1, 612-2, . . . 612-M.

As discussed above, because the channel characteristics can vary overtime, especially in mobile communication system, it can be advantageousto periodically update, or adapt, a set of initial channel estimates. Todetermine updated channel estimates, one can start by reducing Eqs. (8)or (9) to the form of Eq. (22) below: $\begin{matrix}{{{Q_{ii}\lbrack n\rbrack}{{\overset{\sim}{h}}_{i}\lbrack n\rbrack}} = {{p_{i}\lbrack n\rbrack} - {\sum\limits_{g = 1}^{i \neq g}{{Q_{gi}\lbrack n\rbrack}{{\overset{\sim}{h}}_{g}\lbrack n\rbrack}}}}} & (22)\end{matrix}$

Then, when a communication system uses a constant modulus signal such asQAM, the correlation terms Q₁₁[n]=Q₂₂[n]=. . . =Q_(NN)[N]=K and Eq. (22)can be further reduced to Eq. (23) below: $\begin{matrix}{{{\overset{\sim}{h}}_{i}\lbrack n\rbrack} = {\frac{1}{K}\left( {{p_{i}\lbrack n\rbrack} - {\sum\limits_{g = 1}^{i \neq g}\quad{{Q_{gi}\lbrack n\rbrack}{{\overset{\sim}{\quad h}}_{g}\lbrack n\rbrack}}}} \right)}} & (23)\end{matrix}$

Equation (23) suggests that, if each {tilde over (h)}_(g)[n] is known,then the {tilde over (h)}_(i)[n] terms can be determined without amatrix inversion. Unfortunately, given that {tilde over (h)}_(i)[n] isunknown, then {tilde over (h)}_(g)[n] will not likely be known. However,by substituting a previously estimated channel estimate {tilde over(h)}_(g)[n−1] for each {tilde over (h)}_(g)[n] in Eq. (23), Eq. (23) canbe rewritten to the form of Eq. (24): $\begin{matrix}{{{\overset{\sim}{h}}_{i}\lbrack n\rbrack} = {\frac{1}{K}\left( {{p_{i}\lbrack n\rbrack} - {\sum\limits_{g = 1}^{i \neq g}\quad{{Q_{gi}\lbrack n\rbrack}{{\overset{\sim}{\quad h}}_{g}\left\lbrack {n - 1} \right\rbrack}}}} \right)}} & (24)\end{matrix}$

While substituting {tilde over (h)}_(g)[n−1] for each {tilde over(h)}_(g)[n] can cause minor performance degradation, elimination of amatrix inversion using Eq. (24) can lead to major reductions incomputational complexity.

Returning to FIG. 4, it should be appreciated that Eq. (24) suggeststhat the estimator 620 can produce updated channel estimates if theestimator 620 has access to previously determined channel estimates andknown transmitted signals. While the estimator 620 can obviously retainpast channel estimates, the estimator 620 must still find a source forknown transmitted signals.

Fortunately, as discussed above, the diversity gain processor 610 canprovide streams of symbol decisions t′_(i)[n, k] to the estimator 620.If properly equalized, the symbol decisions t′_(i)[n, k] produced by thediversity gain processor 610 are likely the same as the transmittedsymbols t_(i)[n, k]. Accordingly, the estimator 620 can use the streamsof symbol decisions t′_(i)[n, k] as a substitute for t_(i)[n, k] in Eqs.(13)-(16) above and determine sets of updated channel estimates usingEq. (24) above.

As the sets of updated channel estimates are produced, the estimator 620can provide the sets of updated channel estimates to the diversity gainprocessor 610. The diversity gain processor 610, in turn, can use thesets of updated channel estimates to better equalize subsequentlyprocessed data symbols and produce streams of symbol decisions. Thecycle of updating the channel estimates, adaptively equalizing thereceived signals and feeding symbol decisions back to the estimator 620can then continue as required.

FIG. 5 is a block diagram of the estimator 620 of FIG. 4. The estimator620 includes a controller 710, a memory 720 that contains varioustraining symbols 722, a correlation device 730, an approximation device740, a time averaging device 750, a transform device 760, an inputinterface 780 and an output interface 790. The various components710-790 are coupled together by control/data bus 702. Although theexemplary estimator 620 uses a bussed architecture, it should beappreciated that any other architecture may be used as is well-known tothose of ordinary skill in the art.

In a first mode of operation, under control of the controller 710, theinput interface 780 can receive various known symbols via link 152, andstore the received symbols in the memory 720. Next, the controller 710can transfer the received symbols, as well as the training symbols 722to the correlation device 730. The correlation device 730 then cancross-correlate the received and training symbols according to Eqs. (15)or (16) above, and can further correlate the various training symbolsaccording to Eqs. (13) or (14) above to produce first correlationproducts p_(i)[n,l] and second correlation products q_(ij)[n,l]respectively.

The first and second correlation products can then be transferred to theapproximation device 740, where the approximation device 740 can producea set of initial channel estimates according to Eqs. (17)-(21) above.The initial set of channel estimates can then be exported to an externaldevice (not shown) using the output interface 790 and link 622.

While the first mode of operation can produce an initial set of channelestimates using Eqs. (13)-(21) above, it should be appreciated that theinitial set of channel estimates can alternatively be produced by anyother known or later developed technique that can determine or otherwiseprovide initial sets of channel estimates without departing from thespirit and scope of the present invention.

In a second mode of operation, under control of the controller 710, theinput interface 780 can accept other received symbols r_(i)[n, k] vialink 152 and also accept respective decision symbols t′_(i)[n, k] vialink 612, which can then be stored in memory 720.

Next, the controller 710 can transfer the various received symbols anddecision symbols to the correlation device 730, where the correlationdevice 730 can again form various first and second correlation productsaccording to Eqs. (13)-(16) above. The correlation device 730 can thenexport the first and second correlation products to the approximationdevice 740.

The approximation device 740 can receive the first and secondcorrelation products and perform a first pre-estimation processaccording to Eqs. (25) or (26) below to produce sets of pre-estimates{overscore (h)}_(i)[n]: $\begin{matrix}{{{\overset{\_}{h}}_{i}\lbrack n\rbrack} = {{\frac{1}{K}{p_{i}\lbrack n\rbrack}\quad{for}\quad n} = 1}} & (25)\end{matrix}$ $\begin{matrix}{{{{\overset{\_}{h}}_{i}\lbrack n\rbrack} = {{\frac{1}{K}\left( {{p_{i}\lbrack n\rbrack} - {\sum\limits_{g = 1}^{i \neq g}\quad{{Q_{gi}\lbrack n\rbrack}{{\overset{\sim}{\quad h}}_{g}\left\lbrack {n - 1} \right\rbrack}}}} \right)\quad{for}\quad n} = 2}},3,{4\quad\ldots}} & (26)\end{matrix}$

As shown by Eq. (25), if a first block n is being processed, i.e., theestimator 620 is estimating a set of initial channel estimates withouttraining symbols, the set of initial channel pre-estimates areproportional to the first correlation products p_(i)[n]={Σp_(i)[n, l],where l=1, 2, . . . M}. However, for subsequent blocks of data, or whenan initial set of channel estimates has been otherwise provided, theapproximation device 740 can produce various sets of pre-estimatesaccording to Eq. (26). Once the approximation device 740 has determinedthe appropriate sets of pre-estimates, the approximation device 740 canexport the sets of pre-estimates to the time averaging device 750.

The time averaging device 750 can receive the sets of pre-estimates andperform a time averaging operation on pre-estimates to produce sets oftime-averaged estimates according to Eq. (27) below: $\begin{matrix}{{{{\hat{h}}_{i}\left\lbrack {n,l} \right\rbrack} = {{\Phi\quad\left( {{\overset{\_}{h}}_{i}\left\lbrack {n,l} \right\rbrack} \right)} = {\sum\limits_{m = 0}\quad{f_{k}{{\overset{\_}{h}}_{i}\left\lbrack {{n - m},l} \right\rbrack}}}}},} & (27)\end{matrix}$where f_(k) is a time-averaging coefficient. Details abouttime-averaging coefficients can be found in at least “Channel Estimationfor OFDM Systems with Transmitter Diversity” by Li, Y. andAriyavisitakul, S. (U.S. patent application Ser. No. 09/215,074) hereinincorporated by reference in its entirety.

While the exemplary time averaging device 750 uses the approach outlinedby Eq. (27), it should be appreciated that, in various embodiments, thetime averaging device 750 can determine or otherwise approximatetime-averaged estimates according to any known or later developedtechnique without departing from the spirit and scope of the presentinvention.

After the time averaging device 750 produces the sets of time-averagedestimates, the sets of time-averaged estimates can be provided to thetransform device 760 where the transform device 760 can determine setsof updated channel estimates according to Eq. (28) below:{tilde over (H)}_(i)[n,k]=FFT{ĥ[n,l]}  (28)

While the exemplary transform device 760 produces sets of updatedchannel estimates using a fast Fourier transform (FFT), it should beappreciated that any other known or later developed technique orapproach that can determine or otherwise approximate channel estimatesusing time-averaged estimates can be used, such as a direct Fouriertransform, a convolution process and the like, without departing fromthe spirit and scope of the present invention.

After the transform device has produced the various updated channelestimates, the transform device 760 can export the sets of updatedchannel estimates via the output interface 790 and link 622 to anexternal device. The estimator 620 can then repeat the process ofimporting and processing various received symbols and decision symbolsto produce sets of updated channel estimates such that an equalizerusing the updated estimates can adaptively track the changingcharacteristics of various communication channels and extractinformation from various received signals.

FIG. 6 is a flowchart outlining an exemplary technique for producingvarious channel estimates according to the present invention. Theoperation starts in step 810 where a set of initial symbols is received.Next, in step 820, a set of initial channel estimates is produced usingthe received symbols as well as various known training symbols accordingEqs. (13)-(16) above. While the exemplary technique produces initialsets of channel estimates using known training symbols such as trainingsymbols, as discussed above, the sets of initial channel estimatesalternatively can be derived without training symbols using Eqs.(25)-(26) above. In still other embodiments, it should be appreciatedthat the sets of initial channel estimates can be derived or otherwiseprovided by any other known or later developed technique withoutdeparting from the spirit and scope of the present invention. Theoperation continues to step 830.

In step 830, a determination is made as to whether to update, or adapt,the sets of initial channel estimates. If the sets of initial channelestimates are to be adapted, control continues to step 840; otherwise,control jumps to step 890 where the process stops.

In step 840, further received symbols are accepted. Next, in step 845,various respective symbol decisions are also accepted. Then, in step850, the received symbols and symbol decisions are correlated accordingto Eqs. (13)-(16) above to produce first and second correlationproducts. Control continues to step 860.

In step 860, an approximation technique is performed on the first andsecond correlation products to produce sets of pre-estimates accordingto Eqs. (25) or (26) above depending on whether initial sets of channelestimates are available. Next, in step 870, a time averaging operationis performed on the sets of pre-estimates to produce sets oftime-averaged estimates. Control continues to step 880.

In step 880, a transform is performed on the time-averaged estimates toproduce sets of updated channel estimates. While the exemplary transformis a fast Fourier transform, as discussed above, any known or laterdeveloped transform useful to derive or otherwise approximate channelestimates using time-averaged estimates can be used without departingfrom the spirit and scope of the present invention. Control can thenjump back to step 830 where another decision can be taken to update thevarious channel estimates. The various channel estimates can becontinually updated according to steps 830-880 above until it isdesirable or otherwise required to stop channel adaptation.

As shown in FIG. 1-5, the systems and methods of this invention arepreferably implemented on a digital signal processor (DSP) or otherintegrated circuits. However, the systems and methods can also beimplemented using any combination of one or more general purposecomputers, special purpose computers, program microprocessors ormicrocontrollers and peripheral integrating circuit elements, hardwareelectronic or logic circuits such as application specific integratedcircuits (ASICs), discrete element circuits, programmable logic devicessuch as PODs, POAs, FPGAs, PALs or the like. In general, any device onwhich exists a finite state machine capable of implementing the variouselements of FIGS. 1-5 and the flowchart of FIG. 6 can be used toimplement the estimation functions.

While this invention has been described in conjunction with the specificembodiments thereof, it is evident that many alternatives, modificationsand variations will be apparent to those skilled in the art.Accordingly, preferred embodiments of the invention as set forth hereinare intended to be illustrative, not limiting. There are changes thatmay be made without departing from the spirit and scope of the presentinvention.

1. A method of characterizing one or more communication channels,comprising: receiving a set of first symbols associated with a firstcommunication channel; receiving a set of second symbols associated witha second communication channel; and characterizing at least a firstcommunication channel based on at least the set of first symbols and theset of second symbols to produce a set of first channel characteristics;wherein characterizing one or more communication channels is performedwithout a matrix inversion.
 2. The method of claim 1, wherein the set offirst symbols is received from a first transmit device and the set ofsecond symbols is received from a second transmit device.
 3. The methodof claim 2, wherein the set of first symbols and the set of secondsymbols are received using a common receive device.
 4. The method ofclaim 1, wherein at least the first communication channel is based on aconstant-modulus technique.
 5. The method of claim 3, wherein at leastthe first communication channel is further based on an orthogonalfrequency division multiplexing technique.
 6. The method of claim 4,wherein characterizing the first communication channel includes:performing a first correlation to produce a set of first correlations;and determining the set of first channel characteristics based on atleast the set of first correlations.
 7. The method of claim 6, whereindetermining the set of first channel characteristics includesdetermining at least a set of first pre-estimates {overscore(h)}_(i)[n].
 8. The method of claim 7, wherein the set of firstpre-estimates {overscore (h)}_(i)[n] is determined based on theequation:${{{\overset{\_}{h}}_{i}\lbrack n\rbrack} = {\frac{1}{K}{p_{i}\lbrack n\rbrack}}},$wherein p_(i)[n] is the set of first correlations and K is a constant.9. The method of claim 8, wherein characterizing the first communicationchannel further includes time-averaging at least one pre-estimate toproduce a set of time-averaged estimates.
 10. The method of claim 9,wherein characterizing the first communication channel further includesperforming a transform on the set of time-averaged estimates to producea set of channel characteristics.
 11. The method of claim 1, whereincharacterizing the first communication channel includes: performing afirst correlation to produce a set of first correlations; performing asecond correlation to produce a set of second correlations; anddetermining a set of channel pre-estimates based on at least the firstcorrelation product and the second correlation product.
 12. The methodof claim 11, wherein determining the set of first channelcharacteristics includes determining at least a set of firstpre-estimates {overscore (h)}_(i)[n].
 13. The method of claim 12,wherein the set of first pre-estimates {overscore (h)}_(i)[n] isdetermined based on the equation:${{{{\overset{\_}{h}}_{i}\lbrack n\rbrack} = {\frac{1}{K}\left( {{p_{i}\lbrack n\rbrack} - {\sum\limits_{g = 1}^{i \neq g}\quad{{Q_{gi}\lbrack n\rbrack}{{\overset{\sim}{\quad h}}_{g}\left\lbrack {n - 1} \right\rbrack}}}} \right)}},}\quad$wherein p_(i)[n] is related to the set of first correlations, Q_(gi)[n]is related to the set of second correlations, and K is a constant and{tilde over (h)}_(g)[n−1] is related to a set of previously determinedchannel characteristics.
 14. The method of claim 12, whereincharacterizing the first communication channel further includestime-averaging at least one pre-estimate to produce a set oftime-averaged estimates.
 15. The method of claim 14, whereincharacterizing the first communication channel further includesperforming a transform on the a set of time-averaged estimates toproduce a set of channel characteristics.
 16. The method of claim 10,wherein characterizing two or more communication channels does not use amatrix inversion.
 17. The method of claim 10, wherein the first set oftraining signals is transmitted using a first transmit device and theone of the one or more sets of second training signals is transmittedusing a second transmitting device.
 18. An apparatus for communicating,comprising: a receive device that receives at least a set of firsttraining symbols transmitted by a first transmit device and a set ofsecond training symbols transmitted by a second transmit device; and anestimator that estimates at least a first channel related to the firsttransmit device based on at least the set of first training symbols;wherein a cross-correlation between the first set on training symbolsand the sets of second training symbols is essentially zero.
 19. Theapparatus of claim 18, wherein the estimator further estimates the firstchannel based on at least the set of second training symbols.
 20. Theapparatus of claim 19, wherein the estimator estimates the first channelbased without using a matrix inversion.